William Ritchie (1790?–1837) was a Scottish physicist . He was noted as an ingenious experimentalist.
75-512: Augustus De Morgan (27 June 1806 – 18 March 1871) was a British mathematician and logician . He is best known for De Morgan's laws , relating logical conjunction, disjunction, and negation, and for coining the term " mathematical induction ", the underlying principles of which he formalized. De Morgan's contributions to logic are heavily used in many branches of mathematics, including set theory and probability theory , as well as other related fields such as computer science . Augustus De Morgan
150-558: A Unitarian family, where his essentially Christian deist interpretations of scripture were welcome. Later in life he would lean more deist and join Martineau's Free Christian Union . De Morgan was on occasion accused of atheism which he dismissed as sectarianism. In his will De Morgan would write I commend my future with hope and confidence to Almighty God; to God the Father of our Lord Jesus Christ, whom I believe in my heart to be
225-421: A Proposed System of Logic (1860). He showed that reasoning with syllogisms could be replaced with the composition of relations . The calculus was described as the logic of relatives by Charles Sanders Peirce , who admired De Morgan and met him shortly before his death. Historians trace several developments in modern logic directly to De Morgan's contributions to algebraic logic : "Any serious attempt to study
300-461: A confidant on personal matters. The study of logic in Britain underwent a revival following the publication of Richard Whately 's Elements of Logic in 1826. The book itself was the subject of a debate that would spur both De Morgan and George Boole to action. On the one hand, argued by William Whewell , logic, particularly syllogism as emphasized by Whately, could not arrive at "new truths" and
375-659: A consulting actuary for various life assurance firms, including the Family Endowment Assurance Office, the Albert Life Assurance Office, and the Alliance Assurance Company . He published several articles on actuarial subjects as well as the book An Essay on Probabilities and Their Application to Life Contingencies and Insurance Offices . However his most notable work as an actuary is his promotion of
450-533: A few months of his birth. His family moved to England when Augustus was seven months old. As his father and grandfather had both been born in India, De Morgan used to say that he was neither English nor Scottish nor Irish, but a Briton "unattached," using the technical term applied to an undergraduate of Oxford or Cambridge who was not a member of any one of the colleges. When De Morgan was ten years old, his father died. His mathematical talents went unnoticed until he
525-477: A financial economist might study the structural reasons why a company may have a certain share price , a financial mathematician may take the share price as a given, and attempt to use stochastic calculus to obtain the corresponding value of derivatives of the stock ( see: Valuation of options ; Financial modeling ). According to the Dictionary of Occupational Titles occupations in mathematics include
600-641: A full curriculum, from Euclid through the calculus of variations, with his classes often exceeding 100 students. His approach integrated lectures, reading, problem sets, personal instruction, and extensive course notes. He disliked rote learning and viewed mathematics education as learning to reason and core to a liberal education. Several of his students went on to become mathematicians, most notably James Joseph Sylvester , and some of them, Edward Routh and Isaac Todhunter , well known educators themselves. Many of his non-mathematician students rated him highly; William Stanley Jevons described De Morgan as "unrivalled" as
675-464: A government pension. Recruited by Elizabeth Jesser Reid , in 1849 De Morgan taught mathematics for one year at the newly founded Ladies College in Bedfored Square . In 1850 De Morgan received a book from John Elliot Drinkwater Bethune , A Treatise on Problems of Maxima and Minima , written and self-published by the self-taught Indian mathematician Ramchundra . De Morgan was so struck by
750-400: A manner which will help ensure that the plans are maintained on a sound financial basis. As another example, mathematical finance will derive and extend the mathematical or numerical models without necessarily establishing a link to financial theory, taking observed market prices as input. Mathematical consistency is required, not compatibility with economic theory. Thus, for example, while
825-788: A political dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked and scraping off her skin with clamshells (some say roofing tiles). Science and mathematics in the Islamic world during the Middle Ages followed various models and modes of funding varied based primarily on scholars. It was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. Funding for translation of scientific texts in other languages
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#1732794385867900-698: A series of papers "On the foundation of algebra", describing what he called "logical" or " double " algebra, essentially an early form of geometric algebra . While these papers are perhaps most notable for their influence on Sir William Rowan Hamilton and the development of quaternions , they are also recognized to contain De Morgan's steps towards a fully abstract algebra : "Inventing a distinct system of unit-symbols, and investigating or assigning relations which define their mode of action on each other". De Morgan summarized and extended his algebraic work in his book Trigonometry and Double Algebra (1849). De Morgan
975-520: A series of papers and the book Trigonometry and Double Algebra (1849). De Morgan's double algebra was never fully developed but remains a precursor to geometric algebra and influenced the Irish mathematician Sir William Rowan Hamilton in his development of quaternions . De Morgan and Hamilton were friends and correspondents for over 25 years, with De Morgan serving both as a colleague in mathematics, reviewing his Lectures on Quaternions (1853), and as
1050-496: A strict Church of England upbringing De Morgan was publicly a non-conformist , at some personal cost: His refusal to conform debarred him from further advancement at Cambridge; his marriage was without Church ceremony; and on several occasions he fought with the University College administration to maintain religious neutrality, eventually resigning over the issue. In private De Morgan was a dissenter : He married into
1125-601: A teacher. Jevons, heavily influenced by De Morgan, would go on to do independent work in logic and become best known for the development of the theory of utility as part of the so-called Marginal Revolution . In 1866, the Chair of Mental Philosophy and Logic at University College fell vacant and James Martineau was recommended formally by the Senate to the Council. The Council, at the urging of George Grote , rejected Martineau on
1200-420: Is mathematics that studies entirely abstract concepts . From the eighteenth century onwards, this was a recognized category of mathematical activity, sometimes characterized as speculative mathematics , and at variance with the trend towards meeting the needs of navigation , astronomy , physics , economics , engineering , and other applications. Another insightful view put forth is that pure mathematics
1275-451: Is a mathematical science with specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on problems, often concrete but sometimes abstract. As professionals focused on problem solving, applied mathematicians look into the formulation, study, and use of mathematical models in science , engineering , business , and other areas of mathematical practice. Pure mathematics
1350-635: Is also of note, in particular Trigonometry and Double Algebra (1849). De Morgan was also a well known popularizer of science and mathematics; he contributed over 600 articles to the Penny Cyclopedia, ranging from Abacus to Young, Thomas . His most unusual work is A Budget of Paradoxes , a compilation of his writing, mostly book reviews, for The Athenæum Journal . While De Morgan's two early works on algebra are instructional, his translation of Bourdon's The Elements of Algebra (1828) and his own textbook The Elements of Algebra (1835),
1425-400: Is not necessarily applied mathematics : it is possible to study abstract entities with respect to their intrinsic nature, and not be concerned with how they manifest in the real world. Even though the pure and applied viewpoints are distinct philosophical positions, in practice there is much overlap in the activity of pure and applied mathematicians. To develop accurate models for describing
1500-827: The Penny Cyclopedia and contributions to the Quarterly Journal of Education , the Gallery of Portraits , and the Companion to the British Almanac . Following his first resignation from London University, De Morgan started his work as a private tutor. One of his early students was Jacob Waley . He would tutor Ada Lovelace from 1840 through 1842, primarily via correspondence. De Morgan's great-grandfather, grandfather, and father-in-law were all actuaries ; not surprisingly, De Morgan also worked as
1575-585: The Mathematical Tripos , earning a Bachelor of Arts degree. To obtain the higher degree of Master of Arts and become eligible for a fellowship, he was required to pass a theological test. Although he was raised in the Church of England, De Morgan strongly objected to taking this test. Unable to advance in academia due to his refusal, he entered Lincoln's Inn to pursue a career in law. The London University (now known as University College London)
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#17327943858671650-555: The Royal Academy of Tain , in Ross-shire . After saving a little money, he provided a substitute to perform his duties, and went to Paris. There he attended the lectures of Louis Jacques Thénard , Joseph Louis Gay-Lussac , and Jean-Baptiste Biot . He soon acquired skill in devising and performing experiments in natural philosophy . Ritchie's publications led to his appointment to the professorship of natural philosophy at
1725-582: The Royal Institution , where he delivered a course of probationary lectures in 1829. In 1832 he was appointed professor of natural philosophy in London University . Ritchie was subsequently engaged on experiments on the manufacture of glass for optical purposes, and a commission was appointed by the government to inquire into his results. A telescope of eight inches aperture was constructed by John Dollond from Ritchie's glass, at
1800-718: The Royal Society ) but also read and discussed. The first meeting of the London Mathematical Society was held at University College in 1865. De Morgan was the first president and his son was the first secretary. The earliest members included Benjamin Gompertz , De Morgan's personal friend and fellow actuary, William Stanley Jevons and James Joseph Sylvester , De Morgan's former students, Thomas Archer Hirst , De Morgan's colleague, and mathematicians William Kingdom Clifford and Arthur Cayley . Augustus
1875-676: The Schock Prize , and the Nevanlinna Prize . The American Mathematical Society , Association for Women in Mathematics , and other mathematical societies offer several prizes aimed at increasing the representation of women and minorities in the future of mathematics. Several well known mathematicians have written autobiographies in part to explain to a general audience what it is about mathematics that has made them want to devote their lives to its study. These provide some of
1950-478: The graduate level . In some universities, a qualifying exam serves to test both the breadth and depth of a student's understanding of mathematics; the students who pass are permitted to work on a doctoral dissertation . Mathematicians involved with solving problems with applications in real life are called applied mathematicians . Applied mathematicians are mathematical scientists who, with their specialized knowledge and professional methodology, approach many of
2025-550: The Cambridge Philosophical Society in 1846. The paper describes a mathematical system that formalizes Aristotelian logic , specifically the syllogism . While the rules De Morgan defines, including the eponymous De Morgan's laws , are straightforward, the formalism is significant: it represented the first serious instance of mathematical logic, which would come to pervade the field of logic, and presaged logic programming . The subsequent dispute with
2100-586: The Italian and German universities, but as they already enjoyed substantial freedoms and autonomy the changes there had begun with the Age of Enlightenment , the same influences that inspired Humboldt. The Universities of Oxford and Cambridge emphasized the importance of research , arguably more authentically implementing Humboldt's idea of a university than even German universities, which were subject to state authority. Overall, science (including mathematics) became
2175-632: The Royal Society and he never attended a meeting of the Society. He said that he had no ideas or sympathies in common with the physical philosopher; his attitude was possibly due to his physical infirmity, which prevented him from being either an observer or an experimenter. He never voted at an election, and he never visited the House of Commons , the Tower of London , or Westminster Abbey . Despite
2250-503: The Society for 30 years. In 1836, De Morgan's replacement as Professor of Mathematics, George J. P. White, drowned; De Morgan was convinced to return and reinstated. That same year the London University was renamed University College and, together with King's College , was made an affiliate of the newly created University of London . De Morgan was a highly successful mathematics teacher. For over 30 years his courses covered
2325-460: The Son of God, but whom I have not confessed with my lips, because in my time such confession has always been the way up in the world. At age 60, De Morgan's pupils secured him a pension of £500 p.a., but misfortunes followed. Two years later, his son George—the "younger Bernoulli," as Augustus loved to hear him called, in allusion to the eminent father-and-son mathematicians of that name—died. This blow
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2400-657: The Study and Difficulties of Mathematics (1831), Elementary Illustrations of the Differential and Integral Calculus (1832), The Elements of Spherical Trigonometry (1834), Examples of the Processes of Arithmetic and Algebra (1835), An Explanation of the Gnomic projection of the sphere (1836), The Differential and Integral Calculus (1842), and The Globes Celestial and Terrestrial (1845), as well as over 700 articles in
2475-598: The University of London. De Morgan was full of personal peculiarities. On the occasion of the installation of his friend, Lord Brougham, as Rector of the University of Edinburgh, the Senate offered to confer on him the honorary degree of LL. D.; he declined the honor as a misnomer. He humorously described himself using the Latin phrase ' Homo paucarum literarum ' (man of few letters), reflecting his modesty about his extensive contributions to mathematics and logic. He disliked
2550-602: The Warden, Leonard Horner , a dispute arose over the handling of medical student protests calling for the removal of the Professor of Anatomy, Granville Sharp Pattison , on the grounds of incompetence. While De Morgan and others argued that students should have no influence in the matter, the University bowed to student pressure and dismissed Pattison. De Morgan resigned on 24 July 1831, followed by Professors George Long and Friedrich August Rosen . In 1826 Lord Brougham, one of
2625-513: The autumn of 1837, De Morgan married Sophia Elizabeth Frend (1809–1892), the eldest daughter of William Frend and Sarah Blackburne (1779–?), a granddaughter of Francis Blackburne (1705–1787), Archdeacon of Cleveland. De Morgan had three sons and four daughters, including fairytale author Mary De Morgan . His eldest son was the potter William De Morgan , who would marry the painter Evelyn De Morgan , nee Pickering. His second son, George, acquired distinction in mathematics at University College and
2700-478: The best glimpses into what it means to be a mathematician. The following list contains some works that are not autobiographies, but rather essays on mathematics and mathematicians with strong autobiographical elements. William Ritchie (physicist) Born about 1790, he was educated for the Church of Scotland , and was licensed to preach; but he abandoned the church for the teaching profession. He became rector of
2775-503: The contemporary work of Tarski or Birkhoff should begin with a serious study of the most significant founders of their field, especially Boole , De Morgan, Pierce and Schröder ". In fact, a theorem articulated by De Morgan in 1860 was later expressed by Schrŏder in his textbook on binary relations , and is now commonly called Schröder rules . De Morgan was an early convert and supporter of Peacock's symbolical algebra but soon grew disillusioned. Starting in 1839, De Morgan authored
2850-581: The differential and integral calculus (1836; 2nd edit. 1847). He communicated to the Royal Society—of which he was elected a fellow—papers On the Elasticity of Threads of Glass and the Application of this Property to Torsion Balances , and also experimental researches on the electric and chemical theories of galvanism , on electromagnetism , and voltaic electricity . His papers contributed to
2925-525: The effect of the intense Hinduizing of three such men as Babbage, De Morgan, and George Boole on the mathematical atmosphere of 1830–65. What share had it in generating the vector analysis and the mathematics by which investigations in physical science are now conducted? Arthur Cowper Ranyard and George Campbell De Morgan, De Morgan's son, conceived the idea of founding a mathematical society in London, where mathematical papers would be not only received (as by
3000-476: The first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry , by deriving four corollaries to Thales's theorem . The number of known mathematicians grew when Pythagoras of Samos ( c. 582 – c. 507 BC ) established the Pythagorean school , whose doctrine it
3075-500: The focus of universities in the 19th and 20th centuries. Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge. The German university system fostered professional, bureaucratically regulated scientific research performed in well-equipped laboratories, instead of
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3150-1060: The following. There is no Nobel Prize in mathematics, though sometimes mathematicians have won the Nobel Prize in a different field, such as economics or physics. Prominent prizes in mathematics include the Abel Prize , the Chern Medal , the Fields Medal , the Gauss Prize , the Nemmers Prize , the Balzan Prize , the Crafoord Prize , the Shaw Prize , the Steele Prize , the Wolf Prize ,
3225-753: The founders of London University, founded the Society for the Diffusion of Useful Knowledge (SDUK) with the goal of promoting self-education and improving the moral character of the middle- and working- classes through cheap and accessible publications. De Morgan became involved with the SDUK in March 1827; his unpublished manuscript Elements of Statics for the society may have played a role in his appointment to London University. One of its most voluminous and effective writers, De Morgan published several books with SDUK: On
3300-405: The grounds that he was a Unitarian clergyman and instead appointed a layman, George Croom Robertson . De Morgan argued that the founding principle of religious neutrality had been abandoned and immediately resigned. De Morgan was an early proponent of symbolical algebra . First expressed by George Peacock in his Treatise on Algebra (1830) and developed by Duncan Gregory , symbolical algebra
3375-633: The imposing problems presented in related scientific fields. With professional focus on a wide variety of problems, theoretical systems, and localized constructs, applied mathematicians work regularly in the study and formulation of mathematical models . Mathematicians and applied mathematicians are considered to be two of the STEM (science, technology, engineering, and mathematics) careers. The discipline of applied mathematics concerns itself with mathematical methods that are typically used in science, engineering, business, and industry; thus, "applied mathematics"
3450-461: The inclusion of logic in the Cambridge curriculum. De Morgan's paper "On the structure of the syllogism", published in 1846, mathematically defines the rules of Aristotelian logic , specifically syllogism , and including what are now known as De Morgan's laws . Historically significant as the inception of mathematical logic , at the time, De Morgan's paper initiated a dispute with Hamilton over
3525-485: The issues he encountered while writing them would spur his later research. Mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems . Mathematicians are concerned with numbers , data , quantity , structure , space , models , and change . One of the earliest known mathematicians was Thales of Miletus ( c. 624 – c. 546 BC ); he has been hailed as
3600-580: The kind of research done by private and individual scholars in Great Britain and France. In fact, Rüegg asserts that the German system is responsible for the development of the modern research university because it focused on the idea of "freedom of scientific research, teaching and study." Mathematicians usually cover a breadth of topics within mathematics in their undergraduate education , and then proceed to specialize in topics of their own choice at
3675-474: The king of Prussia , Fredrick William III , to build a university in Berlin based on Friedrich Schleiermacher 's liberal ideas; the goal was to demonstrate the process of the discovery of knowledge and to teach students to "take account of fundamental laws of science in all their thinking." Thus, seminars and laboratories started to evolve. British universities of this period adopted some approaches familiar to
3750-534: The philosopher Sir William Stirling Hamilton over the "quantification of the predicate" referred to in De Morgan's paper would lead George Boole to write the pamphlet Mathematical Analysis of Logic (1847). De Morgan elaborated upon his initial paper in the book Formal Logic, or the Calculus of Inference, Necessary and Probable (1847), published the same week as Boole's pamphlet and was immediately overshadowed by it. Nonetheless, later practitioners would recognize
3825-424: The pioneering nature of his work; C. I. Lewis wrote, "His originality in the invention of new logical forms, his ready wit, his pat illustrations, and clarity and liveliness of his writing did yeoman service in breaking down the prejudice against the introduction of 'mathematical' methods into logic". De Morgan developed the calculus of relations in his paper "On the syllogism, No. IV" and in his book Syllabus of
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#17327943858673900-445: The position. Ultimately the search committee, steered by founder Lord Brougham , Olinthus Gregory , and Henry Warburton , selected De Morgan from a field of at least 31 candidates including Dionysius Lardner , Peter Nicholson , John Radford Young , Henry Moseley , John Herapath , Thomas Hewitt Key , William Ritchie , and John Walker . De Morgan's work during this period focused on mathematical instruction: His first publication
3975-531: The probability and likely cost of the occurrence of an event such as death, sickness, injury, disability, or loss of property. Actuaries also address financial questions, including those involving the level of pension contributions required to produce a certain retirement income and the way in which a company should invest resources to maximize its return on investments in light of potential risk. Using their broad knowledge, actuaries help design and price insurance policies, pension plans, and other financial strategies in
4050-469: The provinces outside London, and while his family enjoyed the seaside and men of science were having a good time at a meeting of the British Association in the country, he remained in the hot and dusty libraries of the metropolis. He said that he felt like Socrates , who declared that the farther he was from Athens , the farther he was from happiness. He never sought to become a Fellow of
4125-484: The real world, many applied mathematicians draw on tools and techniques that are often considered to be "pure" mathematics. On the other hand, many pure mathematicians draw on natural and social phenomena as inspiration for their abstract research. Many professional mathematicians also engage in the teaching of mathematics. Duties may include: Many careers in mathematics outside of universities involve consulting. For instance, actuaries assemble and analyze data to estimate
4200-759: The recommendation of the commission, but its performance was not very satisfactory (it is unrelated to the later Ritchey–Chrétien telescope ). Ritchie died on 15 September 1837 of a fever caught in Scotland. He became known to Sir John Herschel , and through him he communicated to the Royal Society papers On a New Photometer , On a New Form of the Differential Thermometer , and On the Permeability of Transparent Screens of Extreme Tenuity by Radiant Heat . Shortly afterwards he published two small treatises on geometry (1833; 3rd edit. 1853) and
4275-509: The role of mathematics in logic; "mathematics can not conduce to logical habits at all," Hamilton would write. The dispute would focus on the so-called quantification of the predicate , which Hamilton claimed, but as the dispute wore on in the pages of the Athenæum and in the publications of the two writers, it became apparent that Hamilton and his supporters were wrong and that De Morgan's mathematically precise description of Aristotle's logic
4350-403: The seventeenth century at Oxford with the scientists Robert Hooke and Robert Boyle , and at Cambridge where Isaac Newton was Lucasian Professor of Mathematics & Physics . Moving into the 19th century, the objective of universities all across Europe evolved from teaching the "regurgitation of knowledge" to "encourag[ing] productive thinking." In 1810, Alexander von Humboldt convinced
4425-550: The work of Benjamin Gompertz , whose " law of mortality " was both under-appreciated and plagiarized. De Morgan became involved with the Astronomical Society of London in 1828. He would be appointed honorary secretary in 1831, the year in which it received its Royal Charter and became the Royal Astronomical Society . He would continue as secretary for 18 years and remain actively involved in
4500-435: The work that he entered into correspondence with Ramchundra and arranged for the book's re-publication in London in 1859, targeting a European audience; De Morgan's preface surveyed classical Indian mathematical thought and urged a contemporary return of Indian mathematics: On examining this work I saw in it, not merely merit worthy of encouragement, but merit of a peculiar kind, the encouragement of which, as it appeared to me,
4575-888: Was Al-Khawarizmi . A notable feature of many scholars working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on optics , maths and astronomy of Ibn al-Haytham . The Renaissance brought an increased emphasis on mathematics and science to Europe. During this period of transition from a mainly feudal and ecclesiastical culture to a predominantly secular one, many notable mathematicians had other occupations: Luca Pacioli (founder of accounting ); Niccolò Fontana Tartaglia (notable engineer and bookkeeper); Gerolamo Cardano (earliest founder of probability and binomial expansion); Robert Recorde (physician) and François Viète (lawyer). As time passed, many mathematicians gravitated towards universities. An emphasis on free thinking and experimentation had begun in Britain's oldest universities beginning in
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#17327943858674650-407: Was The Elements of Algebra (1828), a translation of a French textbook by Louis Bourdon [ fr ] , followed by Elements of Arithmetic (1830), a widely used and long-lived textbook, and The Study and Difficulties of Mathematics (1831), a discourse on mathematical education. Following a series of squabbles between the faculty, including De Morgan, and the administration, in particular
4725-478: Was founded in 1826 as a secular alternative to Oxford and Cambridge; Catholics, Jews, and dissenters could enter as students and hold positions. Prior to opening in 1828, the University advertised 24 vacancies for professorship, two in mathematics, to which De Morgan applied. De Morgan was appointed Professor of Mathematics on 23 February 1828 at the age of twenty-one. The Council of the London University had failed to recruit Charles Babbage and John Herschel to
4800-635: Was a first step towards abstract algebra , separating the manipulation of symbols from their arithmetic meaning. While symbolical algebra could mechanically construct negative and imaginary numbers, as in the work of Adrien-Quentin Buée [ fr ] , Jean-Robert Argand , and John Warren , it could not provide their interpretation; De Morgan observed that a similar problem troubled the classical Indian mathematician Bhāskara II in his work Bijaganita . De Morgan would move on from symbolical algebra to develop what he called "logical" or " double " algebra in
4875-412: Was a prolific writer; an incomplete list of his works occupies 15 pages of his memoirs. While most of De Morgan's mathematical writing is educational in nature, consisting of various textbooks, it is for his pioneering contributions to logic for which he is best known, presented in several books and papers, notably Formal Logic (1847) and Syllabus of a Proposed System of Logic (1860). His work on algebra
4950-587: Was born in Madurai , in the Carnatic region of India , in 1806. His father was Lieutenant-Colonel John De Morgan (1772–1816), who held various appointments in the service of the East India Company , and his mother, Elizabeth (née Dodson, 1776–1856), was the granddaughter of James Dodson , who computed a table of anti-logarithms (inverse logarithms ). Augustus De Morgan became blind in one eye within
5025-593: Was correct. On realizing this, Hamilton would claim that De Morgan had committed plagiarism. Boole, a friend of De Morgan's since 1842, motivated in part by the disputes between Whewell and Hamilton and De Morgan and Hamilton, would write The Mathematical Analysis of Logic , published in 1847 on the same day as De Morgan's Formal Logic . Boole's work would eclipse De Morgan's and come to define early mathematical logic. De Morgan continued to support Boole's efforts, proofreading and advocating for Boole's work. Upon Boole's death, De Morgan worked to ensure Boole's family received
5100-443: Was followed by the death of a daughter. Five years after his resignation from University College, De Morgan died of nervous prostration on 18 March 1871. De Morgan is best known for his pioneering contributions to mathematical logic , specifically algebraic logic , and, to a lesser extent, for his contributions to the beginnings of abstract algebra . De Morgan's contributions to logic are two-fold. Firstly, before De Morgan there
5175-710: Was fourteen when a family friend discovered him making an elaborate drawing of a figure from one of Euclid 's works with a ruler and compasses . He received his secondary education from Mr. Parsons, a fellow of Oriel College, Oxford , who preferred classics to mathematics. In 1823, at the age of sixteen, De Morgan enrolled in Trinity College, Cambridge , where his teachers and tutors included George Peacock , William Whewell , George Biddell Airy , H. Parr Hamilton , and John Philips Higman . Both Peacock and Whewell would influence De Morgan's selection of algebra and logic for further research. De Morgan placed fourth in
5250-410: Was likely to promote native effort towards the restoration of the native mind in India. The influence of classical Indian logic on De Morgan's own work on logic has been speculated upon. Mary Boole , claimed a profound influence—via her uncle George Everest —of Indian thought in general and Indian logic, in particular, on her husband George Boole , as well as on De Morgan: Think what must have been
5325-472: Was no mathematical logic— logic , including formal logic , was the domain of philosophers; De Morgan was the first to make formal logic a mathematical subject. Secondly, De Morgan would develop the calculus of relations, essentially abstracting logic via the application of algebraic principles. De Morgan's first original paper on logic, "On the structure of the syllogism", appeared in the Transactions of
5400-670: Was one of seven children, only four of whom survived to adulthood. These siblings were Eliza (1801–1836), who married Lewis Hensley, a surgeon living in Bath; George (1808–1890), a barrister-at-law who married Josephine, daughter of Vice Admiral Josiah Coghill, 3rd Baronet Coghill ; and Campbell Greig (1811–1876), a surgeon at the Middlesex Hospital. When De Morgan moved to London, he befriended William Frend (1757–1841). Both had studied mathematics at Cambridge and subsequently left for religious reasons, and both were actuaries . In
5475-431: Was ongoing throughout the reign of certain caliphs, and it turned out that certain scholars became experts in the works they translated, and in turn received further support for continuing to develop certain sciences. As these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences. An example of a translator and mathematician who benefited from this type of support
5550-550: Was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypatia of Alexandria ( c. AD 350 – 415). She succeeded her father as librarian at the Great Library and wrote many works on applied mathematics. Because of
5625-559: Was therefore inferior to and distinct from scientific reasoning; on the other hand, argued by the Scottish philosopher Sir William Hamilton , Whately's effort to equate logic to a "grammar for reasoning" was wrong and reductive. De Morgan, perhaps influenced by the writings of Sylvestre François Lacroix , saw the utility of Whately's logic in mathematics, both in its emphasis on the syllogism and in its grammar-like abstraction, as evidenced in his own writings on education and in his demand for
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